Electrostatic chucks are increasingly employed in semiconductor processing equipment as a means for holding a substrate, such as a silicon wafer, in position while undergoing a fabrication process. Skilled artisans will appreciate that electrostatic chucks have a variety of benefits such as an ability to hold a substrate securely in a vacuum chamber where conventional vacuum chucks are inappropriate. An electrostatic chuck can retain a wafer without a need for mechanical retention devices like clips, which can interfere with process conditions, damage the wafer surface, or exclude a portion of the wafer surface from receiving a desired process treatment.
Electrostatic chucks operate by inducing opposing charges on the substrate and the chuck resulting in an electrostatic attraction between the chuck and the substrate. The degree of attraction is dependent on an amount of charge induced as well as a rate at which the charge dissipates due to conductive effects. Voltage biasing is employed to induce and control the electrostatic force and may be applied for only a portion of a processing cycle, e.g., just after a substrate is transferred to the chuck. Alternately, voltage biasing may be applied continuously throughout a processing cycle. For example, using the conduction properties of a plasma can provide a means of electrical connection to one terminal of a substrate and wafer system.
The design and simulation of an electrostatic chuck requires an estimation of several parameters. In particular, the amount of charge which is accumulated between the substrate and the chuck is an important parameter. This charge, known as gap charge, is retained in regions where the substrate and the chuck are not in physical contact. Another important parameter is the electrical resistance between the substrate and the chuck. This resistance, known as gap resistance, is associated with numerous points of contact between the chuck and the substrate. (Skilled artisans will appreciate surface roughness present on both the substrate and the chuck produces a microscopic chuck/substrate interface having many discrete points of physical connection in association with numerous gaps, despite a macroscopic appearance of direct contact.) The gap charge is directly related to the attractive force between the chuck and the substrate, while the gap resistance determines how quickly the attractive force diminishes with time if not maintained by a voltage bias.
When applying a bias to the substrate/chuck system, the gap charge will be affected by charge which is trapped in the chuck itself. This trapped charge is determined by the physical design of the electrostatic chuck in addition to its chemical composition. The trapped charge will further be determined by electrical characteristics of the chuck. In particular, ceramics commonly used by skilled artisans for electrostatic chucks have a grain structure which can provide a resistive path for electrical conduction through the chuck. Additionally, a gap-trapped resistance between the chuck and the substrate can provide an electrical path for trapped charge in the chuck to pass into or out of the substrate according to voltage bias conditions. Finally, the substrate itself will possess a resistance which can affect the charge distribution and time-varying characteristics of the substrate/chuck system.
The design and simulation of electrostatic chucks typically involves the use of experimentally determined values for key design parameters, in particular for the measurements of the charge trapped in the chuck (which will be referred to herein as Ctrapped). In order to model the performance of a chuck having altered design parameters, for example, a different area, new measurements are typically made on a physical system. Furthermore, trade publications and technical articles typically employ simple electrical models for the apparatus used to bias the chuck. These models are usually based on a single constant voltage source and on/off switch with only two resistors and two capacitors.
What is needed is an improved means for electrically modeling the trapped charge in an electrostatic chuck and a method for simulating the effect of trapped charge on electrical parameters which relate to desirable performance characteristics of the chuck such as adhesive force.